def __init__(self, mu, max_entry, multisetvalued=False, setvalued=True):
assert not multisetvalued
self.mu = mu
self.max_entry = max_entry
self.tableaux = list(
Tableau.semistandard(max_entry, mu, setvalued=setvalued))
self._edges = None
self._components = None
self.multisetvalued = multisetvalued
def test_tableaux():
# generate tableaux and reverse plane partitions
from tableaux import Tableau
mu = (4, 2, 1)
a = Tableau.semistandard(3, mu)
b = Tableau.semistandard_setvalued(3, mu)
c = Tableau.semistandard_shifted(3, mu, diagonal_primes=True)
d = Tableau.semistandard_shifted_setvalued(4, mu, diagonal_primes=False)
e = Tableau.semistandard_rpp(3, mu)
f = Tableau.semistandard_shifted_rpp(3, mu, diagonal_nonprimes=False)
# serialize to change a Tableau into a dictionary
s = [t.serialize() for t in c]
def test_semistandard():
mu = ()
assert Tableau.semistandard(0, mu) == {Tableau()}
assert Tableau.semistandard(1, mu) == {Tableau()}
assert Tableau.semistandard(2, mu) == {Tableau()}
mu = (1, )
assert Tableau.semistandard(1, mu) == {Tableau({(1, 1): 1})}
assert Tableau.semistandard(2, mu) == {
Tableau({(1, 1): 1}),
Tableau({(1, 1): 2}),
}
mu = (1, 1)
assert Tableau.semistandard(2, mu) == {Tableau({(1, 1): 1, (2, 1): 2})}
mu = (2, )
assert Tableau.semistandard(2, mu) == {
Tableau({
(1, 1): 1,
(1, 2): 1
}),
Tableau({
(1, 1): 1,
(1, 2): 2
}),
Tableau({
(1, 1): 2,
(1, 2): 2
}),
}
mu = (1, )
assert Tableau.semistandard(3, mu) == {
Tableau({(1, 1): 1}),
Tableau({(1, 1): 2}),
Tableau({(1, 1): 3}),
}
def test_skew_semistandard():
mu = ()
nu = ()
assert Tableau.semistandard(0, mu, nu) == {Tableau()}
assert Tableau.semistandard(1, mu, nu) == {Tableau()}
assert Tableau.semistandard(2, mu, nu) == {Tableau()}
mu = (1, 1)
nu = (1, )
assert Tableau.semistandard(
2, mu, nu) == {Tableau({(2, 1): 1}),
Tableau({(2, 1): 2})}
mu = (2, )
nu = (1, )
assert Tableau.semistandard(2, mu, nu) == {
Tableau({(1, 2): 1}),
Tableau({(1, 2): 2}),
}
mu = (2, 1)
nu = (1, )
assert Tableau.semistandard(2, mu, nu) == {
Tableau({
(1, 2): 1,
(2, 1): 1
}),
Tableau({
(1, 2): 1,
(2, 1): 2
}),
Tableau({
(1, 2): 2,
(2, 1): 1
}),
Tableau({
(1, 2): 2,
(2, 1): 2
}),
}
mu = (2, 2)
nu = (1, )
assert Tableau.semistandard(3, mu, nu) == {
Tableau({
(1, 2): 1,
(2, 1): 1,
(2, 2): 2
}),
Tableau({
(1, 2): 1,
(2, 1): 2,
(2, 2): 2
}),
Tableau({
(1, 2): 1,
(2, 1): 1,
(2, 2): 3
}),
Tableau({
(1, 2): 1,
(2, 1): 2,
(2, 2): 3
}),
Tableau({
(1, 2): 1,
(2, 1): 3,
(2, 2): 3
}),
Tableau({
(1, 2): 2,
(2, 1): 1,
(2, 2): 3
}),
Tableau({
(1, 2): 2,
(2, 1): 2,
(2, 2): 3
}),
Tableau({
(1, 2): 2,
(2, 1): 3,
(2, 2): 3
}),
}
mu = (2, 2, 1)
nu = (1, )
assert Tableau.semistandard(3, mu, nu) == {
Tableau({
(1, 2): 1,
(2, 1): 1,
(2, 2): 2,
(3, 1): 3
}),
Tableau({
(1, 2): 1,
(2, 1): 1,
(2, 2): 2,
(3, 1): 2
}),
Tableau({
(1, 2): 1,
(2, 1): 2,
(2, 2): 2,
(3, 1): 3
}),
#
Tableau({
(1, 2): 1,
(2, 1): 1,
(2, 2): 3,
(3, 1): 3
}),
Tableau({
(1, 2): 1,
(2, 1): 1,
(2, 2): 3,
(3, 1): 2
}),
Tableau({
(1, 2): 1,
(2, 1): 2,
(2, 2): 3,
(3, 1): 3
}),
#
Tableau({
(1, 2): 2,
(2, 1): 1,
(2, 2): 3,
(3, 1): 3
}),
Tableau({
(1, 2): 2,
(2, 1): 1,
(2, 2): 3,
(3, 1): 2
}),
Tableau({
(1, 2): 2,
(2, 1): 2,
(2, 2): 3,
(3, 1): 3
}),
}
def _slow_schur(cls, num_variables, mu, nu=()):
return cls._slow_vectorize(num_variables,
Tableau.semistandard(num_variables, mu, nu))
